Morse theory and local linking for a nonlinear degenerate problem arising in the theory of electrorheological fluids

2014 ◽  
Vol 17 ◽  
pp. 311-321 ◽  
Author(s):  
Vicenţiu D. Rădulescu ◽  
Binlin Zhang
Keyword(s):  
Morse Theory ◽  
Electrorheological Fluids ◽  
Degenerate Problem ◽  
Local Linking ◽  
Nonlinear Degenerate

scholarly journals A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids

2006 ◽  
Vol 462 (2073) ◽  
pp. 2625-2641 ◽  
Author(s):  
Mihai Mihăilescu ◽  
Vicenţiu Rădulescu
Keyword(s):  
Boundary Value Problem ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Electrorheological Fluids ◽  
Mountain Pass Lemma ◽  
Multiplicity Result ◽  
Smooth Bounded Domain ◽  
Degenerate Problem ◽  
Laplace Type ◽  
Nonlinear Degenerate

We study the boundary value problem in , u =0 on , where is a smooth bounded domain in and is a -Laplace type operator, with . We prove that if λ is large enough then there exist at least two non-negative weak solutions. Our approach relies on the variable exponent theory of generalized Lebesgue–Sobolev spaces, combined with adequate variational methods and a variant of the Mountain Pass lemma.

scholarly journals Entropy solutions for an adaptive fourth-order nonlinear degenerate problem for noise removal

2021 ◽  
Vol 6 (4) ◽  
pp. 3974-3995
Author(s):  
Abdelgader Siddig ◽  
◽  
Zhichang Guo ◽  
Zhenyu Zhou ◽  
Boying Wu ◽  
...  
Keyword(s):  
Fourth Order ◽  
Noise Removal ◽  
Entropy Solutions ◽  
Degenerate Problem ◽  
Nonlinear Degenerate
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